5 ms·
Blue isn't only for N=2; it starts showing up again at N=104. It appears that circles are colored blue if their number of contacts (with either other circles o
by JonathonW 7y ago
Blue isn't only for N=2; it starts showing up again at N=104.
It appears that circles are colored blue if their number of contacts (with either other circles or the outside) is equal to 1 or 2. They're magenta if their number of contacts is zero.
I'm not sure what the distinction between orange and yellow is-- it doesn't seem to be strictly number of contacts, because I can see cases where both orange and yellow have four contacts.
- robocat 7y agoReread my answer for orange, I'm sure it is correct. To say it a different way: a circle X is coloured orange if X is touching a circle Y, and both X and Y also touch circle Z. Y and Z can either be small circles or the main outer circle. The colours are about constraints. Orange is a locked constraint between 3 circles (inner and outer included). If you think about it, N=2 is the only solution that the circles are constrained to touch in two places (and N=1 is weird because it touches in infinite places). At N=104, the blue circles are surely a drawing fault, they are actually unconstrained and should be magenta. Shown by fact that those blue circles have a dot in the middle (not touching), but a neighbour circle has a line pointing to the blue circle (touching), which is contradictory.
- showdead 7y agoFor N=104, if you look at the PDF and zoom in, you can see the blue circles have a line rather than a dot. Admittedly, it is hard to see why the blue circles do not have enough freedom to move slightly away and become magenta (particularly the one on N=108).